A fuel pump for a liquid fuel injection system of a motor vehicle is provided. The fuel pump for a fuel injection system includes a low-pressure pump that provides liquid fuel from a fuel tank of the motor vehicle at a low pressure. A high-pressure pump in fluid communication with the low-pressure pump and compresses the liquid fuel from the low pressure to a high pressure for injecting the liquid fuel into an internal combustion engine of the motor vehicle. A pump drive drives the low-pressure pump and the high-pressure pump synchronously with a pump frequency independently from an engine speed of the internal combustion engine of the motor vehicle.